Work done on a gas as volume decreases

AI Thread Summary
The discussion focuses on calculating the work done on a gas as its volume decreases from infinity to zero, using the pressure function P=e-v2. The work is expressed as dW = PdV, leading to the integral W=∫0∞e-v2dV. The solution references the Gaussian integral, concluding that W=(√∏)/2. Participants seek confirmation on the correctness of this calculation. The conversation emphasizes the application of mathematical principles in physics to derive the work done on the gas.
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In a mathematical model, a gas is under a pressure of the form P=e-v2 (v is volume). Find the work (in Joules) done on the gas as its volume decreases from infinity to zero.



dW = PdV



Solution Attempt:
W=∫0∞e-v2dV

http://en.wikipedia.org/wiki/Gaussian_integral

Gaussian Integral=∫-∞∞e-x2dx=√∏

∴∫0∞e-v2dV

=(√∏)/2|∞0

W=(√∏)/2

Is this correct?
 
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